Strange metals and planckian transport in a gapless phase from spatially random interactions

Abstract: Strange' metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ($T$) resistivity to survive down to low temperatures where phonon and Umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions such as large-$N$ limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a non-perturbative regime, using numerically exact high-performance large-scale hybrid Monte Carlo and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals' key experimental signature of linear-in-$T$ resistivity with a universalplanckian' transport scattering rate $\Gamma_\mathrm{tr} \sim k_B T/\hbar$ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point, and instead arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: a feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated electron materials.